What is the difference between applying shallow-learning methods repeatedly and deep learning?
Quite surprising to find someone reading this same book. I read this part a week ago and the explanation is quite clear in the book :

If you use successive shallow learning methods, you first train one model, then you train another model with the outputs of your first model, and then a third with the outputs of your 2nd model. The problem with that is that each model is trained to get good results at his task, not to send information, so there can be an increase when adding successive models, but it is a very weak increase.
If you use deep learning, all the layers are trained at the same time, so each layer learns how to efficiently transfer important information to the next layer of the model. This is why it is much more efficient.

Hope I made it clearer